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arXiv · 1302.3394

On the Singular Scheme of Split Foliations

Maurício Corrêa Jr·Marcos Jardim·Renato Vidal Martins
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Abstract

We prove that the tangent sheaf of a codimension one locally free distribution splits as a sum of line bundles if and only if its singular scheme is arithmetically Cohen-Macaulay. In addition, we show that a foliation by curves is given by an intersection of generically transversal holomorphic distributions of codimension one if and only if its singular scheme is arithmetically Buchsbaum. Finally, we establish that these foliations are determined by their singular schemes, and deduce that the Hilbert scheme of certain arithmetically Buchsbaum schemes of codimension $2$ is birational to a Grassmannian.

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Maurício Corrêa Jr, Marcos Jardim, Renato Vidal Martins. 2014-04-10. On the Singular Scheme of Split Foliations. https://doi.org/10.1512/iumj.2015.64.5672

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